Why is the critic network in the AC algorithm doesn’t have action path like it does in the DDPG algorithm ?

I am currently working on answering this question before moving forward and apply the AC algorithm, I noticed that difference when I was migrating from the DDPG algorithm to the AC algorithm, the reason for why I am migrating to AC, that’s because I need discrete actions for controlling my stepper motor, instead of DDPG continuous actions, which is suitable for DC motor, the stepper motor would have 3 actions [move_right, move_left, no_move], I will provide more details while trying to answer this question, stay tuned.

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